Very quick TLDR about the historical figures, so I won't need to explain who is who in the text.
Kondo Isami: commander of the Shinsengumi and Nagasone's former master. He was an adopted son of the head of the Shieikan dojo and later succeeded his position. His birth name was Katsugoro, which is why Hijikata in the play calls him "Kacchan" before switching to the formal "Kondo-san" when they formed Shinsengumi. He was a fan of forty-seven ronin, which is why the Shinsengumi uniform uses the dandara pattern, and subsequently why Magoroku Kanemoto is interested in them, since he finds it peculiar that he is associated with two groups with the same pattern. Kondo was executed on charges of being involved in the assassination of Sakamoto Ryoma (Mutsunokami's former master), though due to testimonies obtained some time after the execution, it is generally believed that a different group was behind the assassination. After his execution, Kondo's head was on display for a while before someone stole it. The mystery of his missing head is addressed in Shinken Ranbu Sai 2017 concert and the 5th main musical, Musubi no Hibiki, Hajimari no Ne.
On a less serious note, Kondo was known for being able to put his fist in his mouth (it's referenced in Utaawase).
Hijikata Toshizo (Kondo calls him Toshi): the vice-commander of the Shinsengumi and the former master of Izuminokami and Horikawa. He was born in Ishida village, and he has spent his youth selling Ishida powder, his family's all-purpose medicine that may or may not have had any effect. He was enrolled in the Shieikan dojo and went with Kondo to Edo. In the Shinsengumi, he was known as the Demon Vice-Commander who was enforcing their strict code. He wrote poetry but wasn't very good at it. After Kondo's execution, he led the remnants of the Shinsengumi until his own death. His life after Kondo's execution will be covered in the 5th musical, Musubi no Hibiki, Hajimari no Ne.
Credits for haiku translations: the first one (Izuminokami's) by @sohmariku, the second one (Hijikata's) by @strifescloud
Okita Soji: the captain of the Shinsengumi's first unit and the former master of Kashuu and Yamatonokami. Another pupil of Shieikan dojo, but, unlike Kondo and Hijikata, he was a samurai by birth. While Okita did collapse during the Ikedaya raid, it is disputed if it was due to tuberculosis. He died a couple of months after Kondo, and the people that were taking care of him made sure he didn't know about the execution. At one point in the play, Okita will be associated with the 16-petal chrysanthemum. This particular symbol is significant due to being the mon of the Imperial family (Shinsengumi was pro-shogunate), though I think it is supposed to represent the legend of Okita owning a Kiku (=chrysanthemum) Ichimonji instead. So, who knows, maybe Norimune was another hidden sword in this production!
Shinsengumi: a police organization from Kyoto with a short but rather turbulent history. In 1863, Kondo and others went to Edo to guard the shogun on his visit to Kyoto, but afterwards, instead of returning to Edo, some of the men remained in Kyoto. They formed Mibu Roshigumi and lived in Mibu village, where they weren't popular with the locals, who called them "Wolves of Mibu". Eventually, the group was reformed into the Shinsengumi. "Shinsengumi" means "newly selected corps", which ties into the chosen/unchosen theme of the play. Nagakura Shinpachi (captain of the 2nd unit) and Todo Heisuke (captain of the 8th unit) are named extras, though they don't do anything beyond filling space. They were also Shieikan pupils and founding members of the Shinsengumi, but Todo was eventually killed by his fellow Shinsengumi members due to disagreements within the group, while Nagakura is one of the few Shinsengumi survivours who got to live till old age and he is one of the primary sourses for what we know about the group.
While undercover as "Okizawa", Yamatonokami probably took place of Okuzawa Eisuke, one of the Shinsengumi casualties of the Ikedaya raid.
8 July 1864, Kyoto, Ikedaya. A group of scheming ronin is attacked by the Shinsengumi. Kondo Isami leads the raid, followed by Nagakura Shinpachi, Todo Heisuke and others. During the fight, Okita Soji starts coughing blood and becomes vulnerable to the rebels' attack, but Kondo reaches him in time. As he suspected, Okita has tuberculosis, but Okita asks him not to worry. At the same time, Hijikata Toshizo's unit regroups with Kondo's unit, and Hijikata goes to help Kondo and Okita. Together, they fight off the rebels, bantering and bickering all the while.
(There is a cool scene transition, where the Shinsengumi Touken Danshi appear and do the exact battle moves as their respective masters, which leads into the main theme song)
At Honmaru, Kashuu Kiyomitsu spars with Yamatonokami Yasusada. Since they used to belong to the same master, their fighting styles are so similar, it's almost like they are fighting themselves; they couldn't shake off Okita's habits, but, at the same time, it makes it easier to spot their own shortcomings. They want to spar with Nagasone Kotetsu next, however, Nagasone reminds them that they are supposed to be on the horsekeeping duties right now. Instead, Nagasone spars with Hachisuka Kotetsu, who isn't very pleased with the arrangement. Hachisuka leaves after a short fight, and now it's Izuminokami Kanesada's turn to ask Nagasone for a sparring. Nagasone declines and reminds him about his field duties before leaving. Horikawa Kunihiro catches up to Izuminokami and reprimands him for not finishing his tasks, but Izuminokami is more concerned about the rift between the two Kotetsus. One is an authentic Kotetsu that was passed as an heirloom in the prestigious Hachisuka clan; the other is a fake Kotetsu that was used in battles by the Shinsengumi commander Kondo Isami. It's no wonder they can't find the common ground… but that thought will have to wait, because there is a signal to gather before the mission.
The Saniwa dismisses Kashuu as the captain of the first unit, but asks him to remain as a part of the team. This time the captain will be Hachisuka, who has been around for a long time, but never acted as a captain. Kashuu congratulates Hachisuka, and the Saniwa calls the Shinsengumi swords to join the team, since the Shinsengumi is believed to be the next target of HRA. Hachisuka expresses his problems with this formation: first, he feels there are more suitable candidates to lead a Bakumatsu mission; second, he doesn't understand why he would be put in the same team as the fake Kotetsu. Nagasone just accepts that the Saniwa must have his own reasons, and, after being reminded of their duties, the team is sent to the past.
February 1863, Bushu province, Tama district. It's the first time the Okita swords visit this place, since, when the Shinsengumi returned to Edo in 1868, Okita wasn't with them anymore. But at this point in time the Shinsengumi doesn't even exist yet. Kondo and Hijikata were born around here, so the Touken Danshi conclude they might be targeted by the HRA to prevent the formation of the Shinsengumi. The team's musings are interrupted by the future Shinsengumi members passing by. Okita is making fun of Hijikata and his Ishida powder, but admits that he knows that Hijikata is selling this "all-purpose medicine" to repay Kondo's adopted father's kindness. Angered, Hijikata runs after Okita, with laughing Kondo following after them. Horikawa explains to Hachisuka who those people were, and Yamatonokami notes Okita's healthiness. However, it's not a good time to reminisce, since the team senses the HRA nearby. During the skirmish, the Kotetsus can't fight in sync; they get in each other's way, and Hachisuka gets offended when Nagasone protects him. Afterwards, the Kotetsus separate to cool their heads, with the Hijikata swords going after them. Yamatonokami muses that if they would've joined the Shinsengumi, they could've spent more time with Okita, but Kashuu says it won't be possible. After Kashuu leaves, Yamatonokami sees the moment when Kondo was offered to join the group that would guard the shogun during his visit to Kyoto, with Kondo, Hijikata, Okita and Todo all raring to go. After the others leave, Okita says that he will be happy as long as Kondo and Hijikata are happy, and, as he leaves, a ghostly black cat appears under the evening skies with visible Sirius.
At night, the Hijikata swords discuss the Kotetsus. Izuminokami thinks things will settle themselves over time, but Horikawa wants to more actively help two brothers to reconcile. He tries to approach Nagasone, but Nagasone isn't used to talking about his feelings and leaves. He then tries his luck with Hachisuka, who turns out to be more personable than he expected. Horikawa suggests to Hachisuka to try to be more relaxed; after all, no matter his origins, by now he has seen as much fighting as the rest of the team. Hachisuka thanks him for the advice and apologizes for his failings as the captain. Horikawa assures him that he is doing fine, and if Hachisuka has any questions, he will be happy to answer, since it's in his nature as a wakizashi to help others. Hachisuka takes him up on his offer and asks about what the Shinsengumi swords feel towards their former masters. Horikawa tells him how, since they were bound by the same circumstances and ideals, they never fought alone, and that this spirit of comradery is still with the Shinsengumi swords. As the Shinsengumi were among the last people to use swords in battle, it's no wonder that their swords like them a lot. However, this is something that Hachisuka can't relate to, because he spent all his time on display rather than in battle. Horikawa understands that he talked himself into a corner and decides to use his trump card: a drinking party!
Fighting wasn't the only thing the Shinsengumi did in Kyoto, and their swords aren't going to let their sillier traditions die. Izuminokami gives Hachisuka a HUGE mug (seriously, that thing can probably contain as much liquid as the other five cups combined), while Horikawa fills it to the brim with sake bought on Izuminokami's dime. As the party starts, the Okita swords try to have a drinking contest, but it gets interrupted by Izuminokami, who is already drunk after one cup. Yamatonokami asks Hachisuka if he can hold his liquor, and Hachisuka proves himself by drinking his entire mug in (almost) one sitting as everyone cheers him on. Next, Izuminokami comes up with a brilliant haiku: "Cherry trees at night. As I watch them all alone. I just want to sleep." After Izuminokami is put to sleep, Nagasone performs Kappore, a comedic dance that was popular during the Bakumatsu and Meiji periods, with Nagasone singing about Sirius (known in Japan as "celestial wolf"), the rest of the Shinsengumi swords joining the dance as his pack of wolves, and Hachisuka continuing to drink on the side (but he does do the "wolf paws" pose with the rest).
In the morning, Yamatonokami tries to sneak out of the camp, but runs into Kashuu, who quickly realizes why he wants to leave. Their argument wakes everyone else up, and Yamatonokami admits that he wants to join the Shinsengumi. He makes an excuse that the enemies may try to infiltrate them, but everyone else is against it, because it is both dangerous and may lead to changes in history. When Izuminokami points out that he may even break, Yamatonokami shouts that he isn't that weak, and when Kashuu tries to stop him, Yamatonokami gets upset because Kashuu was chosen by Okita during the Ikedaya raid, while Yamatonokami feels guilt for not being there when Okita needed him most. Nagasone asks Izuminokami to go after Yamatonokami, while angry Kashuu leaves on his own, and Horikawa explains the situation to Hachisuka.
Everyone has their own thoughts about being chosen (or not). Hachisuka wasn't chosen for the battlefield, while Nagasone had no choice but to take many lives. Kashuu lives with the memory of Okita's blood and doesn't want anyone else to experience something like that, while Yamatonokami wanted to always be by Okita's side no matter what. Unlike them, even though Izuminokami had no choice but to be separated from Hijikata, he accepts that and feels nothing but pride. In the end, even their masters weren't chosen by the times, as they fought on the losing side and died early deaths.
But now that they have their own bodies, they want to make their own choices. Kashuu asks Hachisuka to let Yamatonokami join the Shinsengumi. Having emotions might be inconvenient, but thanks to them, he can understand Yamatonokami's feelings. Hachisuka tells him that perhaps Yamatonokami would have loved to hear that, but Kashuu doesn't want to say it to him.
Hachisuka decides that he should stop being so pessimistic. Even if he wasn't used on the battlefield, he was cherished by his former masters, and this is something he is proud of. If the Saniwa chose him for this mission, there must be something only he can do.
To the surprise of everyone (minus Kashuu), Hachisuka approves Yamatonokami's plan to join the Shinsengumi. There is a chance that the group will be attacked, and even if Yamatonokami accidentally does something to change history, the rest of the team just needs to make sure it won't be recorded. To minimize the effect on history, Yamatonokami is forbidden from standing out, must live among the humans, and can't talk with his former master. Yamatonokami agrees with these conditions, since they don't contradict his desire to protect Okita. Nagasone tries to protest, but Hachisuka points out that members of the Shinsengumi wouldn't question their commander.
November 1863, Kyoto, Mibu. The black cat once again oversees human lives: Kondo, Hijikata and Okita have become a part of the newly formed Shinsengumi, and Okita once again makes fun of Hijikata's Ishida powder… or rather the fact that he doesn't wear his backpack filled with it anymore. Now that Kondo is their commander, Hijikata promises to support him even if he will become a demon in the process. Kondo laughs at the idea of a demon vice-commander, and promises that, even if everyone else will call him that, Hijikata will always be "Toshi" to him. After the others leave, Hijikata sees "Okizawa" (undercover Yamatonokami) and comments on how gloomy he is. Once alone, Yamatonokami looks at a medicine bottle, but quickly hides it when Horikawa approaches him for his report (and elaborate high-five).
Mibu Temple. Alone, Okita muses that, for Kondo and Hijikata to become true samurai, the Shinsengumi needs to perform great feats. It is Okita's dream to help them get promoted, which is why he wants to master his swordsmanship. Okita reveals that he noticed "Okizawa" watching him, and, after commenting on how quiet he is, he invites Yamatonokami to join his training. Okita is surprised that he can match his moves so well, which makes Yamatonokami happy. After finishing sparring, Okita suddenly deepens his voice to say something that Kondo used to tell him: there is no desire in your sword to protect yourself, and at this rate even nine lives won't be enough for you. Yamatonokami gets upset and confused, but Okita clarifies that he just doesn't want him to act recklessly and invites him to train together some other time. After Yamatonokami leaves, Okita gets a coughing fit, with the cat continuing to watch.
At night, Kashuu approaches stargazing Hachisuka. Kashuu explains that the brightest star in the sky is Sirius, the wolf star. Hachisuka is having doubts about his decision and asks Kashuu if he is worried about Yamatonokami. Kashuu reassures him that no matter if it was right or wrong, he is grateful for it, and wonders if it was all part of the Saniwa's plan. He believes that, even if any of them made mistakes, the Saniwa would still approve of their decisions; they just need to own up to them and fix the problem. Their chat is interrupted by worried Horikawa, who spotted Yamatonokami's medicine bottle and thinks he wants to change history. However, Kashuu believes in him, and on the off chance his trust is misplaced, he asks Hachisuka to let him kill Yamatonokami himself. The gathering is interrupted again by Izuminokami and Nagasone revealing that the enemies will likely strike during the upcoming Ikedaya raid.
8 July 1864, Kyoto, Gion. At the Shinsengumi gathering, Hijikata reports that they can't pinpoint the exact location of the rebels, with Ikedaya and Shikokuya being the most likely choices. Kondo splits his men into two groups: Okita, Nagakura, Todo and "Okizawa" go with him to Ikedaya, while everyone else follows Hijikata to Shikokuya. Hijikata disagrees with such an uneven split, but Kondo stresses that it is his order as the commander. After Hijikata leaves, Okita jokes that someone may die tonight. Kondo laughs him off, but tells him to stay by his side. After everyone leaves, Okita notes that he is still no match for Kondo.
HRA is indeed targeting the raid, so Touken Danshi engage them in combat. The raid proceeds according to history up until the point when Okita collapses. As he starts coughing, the black cat appears on the side, and Okita notes that he can't see Sirius, a winter star, during summer. Yamatonokami runs to his side, agonizing over whether he should give him medicine or not. In the end he chooses not to, which dispels the cat. Yamatonokami admits that he wanted to be closer to Okita, and he has been thinking about scenarios where he would survive and how it would turn out. But now he realized that Kashuu didn't want him to go to Okita's side because he didn't want Yamatonokami to be hurt. Yamatonokami accepts that this is Okita's story and he wouldn't be the same Okita if he changed it. He is glad that he got to spend more time with Okita and thanks him for choosing him as his sword, since he was able to meet "that person."
As Yamatonokami says his final thanks, HRA reach the room with collapsed Okita. Yamatonokami protects him, leaving only when Kondo catches up. Hachisuka reunites with Yamatonokami, and Yamatonokami tells him he is thankful he was able to be with Okita this time after he wasn't chosen in the past, and he is thankful to Hachisuka for making it happen.
Fighting continues on both the Shinsengumi and the Touken Danshi sides. After dispatching some enemies, Kashuu and Yamatonokami agree that the real reason Okita brought Kiyomitsu with him and not Yasusada was pure chance. Kashuu talks with Nagasone about how he might have his regrets, but only the Kashuu of this era has the right to voice them. During one of the skirmishes, Nagasone suggests to Hachisuka to regroup with the rest of the team, but Hachisuka rushes into the fight, and, while he manages to defeat a bunch of enemies, he would have been injured if Nagasone hadn't taken a hit for him. Nagasone isn't damaged too seriously, but the team doesn't have the time to help him because the Shinsengumi are catching up.
Kondo fights off rebels to protect weakened Okita until they reunite with Hijikata. Okita jokingly asks if he brought any Ishida powder, which slightly reassures Hijikata, since, if he still has the strength to have final words, he isn't dying yet. The trio then proceeds to fight more rebels (in slo-mo!).
On the Touken Danshi side, Hachisuka questions Nagasone about why he saved him. It's their job as swords to defeat the enemies, and, moreover, that was the way the Shinsengumi fought. Nagasone doesn't deny it, but points out that the Shinsengumi died in the end. Nagasone thinks what he did was right, but Hachisuka disagrees and leaves. Nagasone tries to go after Hachisuka, but his injuries catch up to him, so Izuminokami carries him away on his back after advising him to try to put his feelings into words (Yamatonokami also wants a piggyback ride but doesn't get one).
Hachisuka thinks about how he was the one who built the wall between him and Nagasone until his introspection is interrupted by a sudden attack from Izuminokami. Izuminokami calls his look gaudy, but praises his fighting once the impromptu sparring starts. As far as Izuminokami is concerned, both good looks and fighting abilities can be practical for a sword, which is why he is at an advantage, since he excels at both. He reassures Hachisuka that being put on display isn't that bad, but this isn't what bothers him at this point. Hachisuka is having trouble reconciling Nagasone's distaste for battle with his desire to protect others. Izuminokami tells him that even though Nagasone is strong, he is also sad. Based on his former master, Izuminokami concludes that there is always a reason for someone to be strong: they are strong because they have no choice but to be strong. There is even a saying about it among humans: the more someone suffers, the stronger they get. Hachisuka doesn't understand why Nagasone wouldn't talk about his sadness, to which Izuminokami replies he should just try to ask him. Why is he so strong? Why is he so sad? After all, if he never asks, he will never understand. Hachisuka thanks him for his advice, but disagrees with Izuminokami's assessment that he and Nagasone are pretty similar. After Hachisuka leaves, Horikawa reveals he saw the scene and starts giggling to Izuminokami's chagrin.
1868, Edo, Sendagaya. Kondo and Hijikata visit Okita, who is greatly weakened by his illness. Hijikata brought him some Ishida powder to get better, and Okita is happy to see that he and Kondo are wearing samurai clothes now. Okita wonders if they will see Sirius tonight. Hijikata is confused by the question, so Okita explains: right after the Shinsengumi was formed, Okita was upset that people disdained them as Wolves of Mibu. But Kondo decided it was perfect. The brightest star in the night sky is called "celestial wolf", so they should be just like it: the wolves that bring light to the world. Unfortunately, Okita starts coughing and finally admits how powerless he now feels. Hijikata tells him it's too early to give up, so he should beat his illness and catch up with him and Kondo. They agree to meet again, even though all three understand they won't be able to keep this promise. Later, Kashuu and Yamatonokami watch Okita having a coughing fit. Kashuu thinks about consoling Yamatonokami, but decides against it.
Hachisuka approaches stargazing Nagasone to ask why he calls himself "Kotetsu" even though he is aware he isn't a real deal. Nagasone explains that there is only one reason he would do something like that: it is the name his former master gave him, and thus Nagasone wants to honour it and work even harder than a real Kotetsu would. His former master took inspiration from the starlight that takes a long time to reach Earth, and he will do the same. Meanwhile, Hachisuka wonders what he will find if he reaches out to Nagasone, but doesn't do it.
April 1868, Shimousa, Nagareyama. Kondo admires Sirius in the moonless sky. He tells Hijikata that Sirius is the second brightest star after the sun, and the implications aren't lost on Hijikata. The Shinsengumi quarters are surrounded, and Kondo decided to surrender himself to let the others escape, even though Hijikata would rather stay and fight to death. Hijikata is shocked, even slipping into calling Kondo "Kacchan" again. But despite his tearful pleas, Kondo doesn't change his mind. For him, Hijikata and Okita are like little brothers, so he can't let them die before him. Kondo gives his last order to his vice-captain: "Never give up!" Hijikata replies to his commander: "Until we meet again!"
Hachisuka witnessed the farewells, but his thoughts are interupted by Horikawa. They have discovered the enemy's next target: Itabashi, the place where Kondo will be executed. Hachisuka asks if Nagasone is alright with that, but Nagasone just answers that their job is to defeat those who try to change past. After others leave, Izuminokami points to Hachisuka that this is very sad.
May 1868, Edo, Sendagaya. Heavily sick Okita is approached by the black cat that suddenly starts talking in a distorted voice. Okita tries to attack it, to no effect. The cat tells him that Kondo is going to be executed soon, and since Okita is so weak, he can borrow the cat's powers to go after him. A 16-petalled chrysanthemum appears over his sword, and Okita gets enough strength to head towards Itabashi.
17 May 1868, Itabashi. Under the heavy rain, Kondo is led to the execution site. Nagasone watches his bound former master, but doesn't let others worry about him since the enemies may strike at any moment. Sure enough, they quickly end up under attack. At one point Nagasone is about to be attacked, but Hachisuka takes a hit for him, even calling out his name for the first time. Now that they are even, their teamwork is a lot better than it was back at the start.
Even though the Touken Danshi managed to drive the enemies off, they are blindsided by a new addition. As the executioners prepare to cut off Kondo's head, they are attacked by Okita. Okita frees Kondo and tries to attack the Touken Danshi who try to talk him down. Yamatonokami reassures him that his life and ideals will be remembered and he doesn't have to fight anymore. However, Okita doesn't want to listen and keeps waving around his possessed sword… until Kondo sheathes it. Kondo tells him they have fought enough and they should just wait for Hijikata on the other side. Okita jokes that knowing him, they will wait for a long time. Kondo suggests to practice swordsmanship while they wait, and Okita agrees that it will be just like the old times. After Okita collapses, Kondo holds him for a while and then entrusts him to Yamatonokami, whom he recognizes as "Okizawa". Kondo asks him to take Okita back to Sendagaya to live his last days, and Yamatonokami and Kashuu leave with unconscious Okita. Kondo then asks Nagasone, who feels familiar to him, to finish the job and take his head. Nagasone agrees, but first asks him a question: why didn't he fight despite being so strong? Kondo answers that he always fought for a better future, and he always intended for Hijikata to inherit his soul. He then asks Nagasone a question of his own: what will become of the Shinsengumi in the future? Nagasone (and the rest) is surprised, but answers that they will become the ray of hope that illuminates the darkness. Satisfied, Kondo lets him proceed with the execution. But before Nagasone can swing his sword, he is backhanded by Hachisuka. Hachisuka tells him that this is exactly what he hates about Nagasone: he always tries to do things by himself even when he has other people he can rely on. Nagasone finally lets himself break down, and, as he cries, Hachisuka cuts Kondo's head off.
Back at Honmaru, Kashuu and Yamatonokami have a sparring. Yamatonokami improved after his training with Okita, while Kashuu is still as picky about non-combat duties as ever. As Yamatonokami drags Kashuu to have a farming contest with him, Hachisuka and Nagasone take their place at the training grounds. Nagasone nervously asks him for a sparring, and Hachisuka agrees. Hachisuka still doesn't acknowledge Nagasone as his brother, but their relationship definitely improved, to the delight of Hijikata's swords. Horikawa tells Izuminokami that Sirius is a binary star: even though you can only see one star with naked eye, there is actually a second star that supports it. This reminds Izuminokami of Hijikata's haiku "Two hearts, opposite, mirror each other, clear as reflected water." After all, everyone has a person like that in their life.